Properties

Level 10
Symmetry even
Weight 0
Character \( \chi_{10}(1,\cdot) \)
Multiplicity 1
Precision 0
Fricke Eigenvalue -1
Atkin-Lehner Eigenvalues n/a

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Spectral parameter

$R= 28.0335697639$

The first few Fourier Coefficients

n c(n)
0  0
1 1
2 0.707106781
3 -0.777023072
4 0.5
5 -0.447213595
6 -0.549438284
7 -1.000331020
8 0.353553390
9 -0.396235144
10 -0.316227766
11 -1.087114703
12 -0.388511536
13 0.187252101
14 -0.707340848
15 0.347495282
16 0.250000000
17 1.832980088
18 -0.280180557
19 0.420332313
20 -0.223606797
21 0.777280283
22 -0.768706179
23 0.704277877
24 -0.274719142
25 0.200000000
26 0.132407231
27 1.084906922
28 -0.500165510
29 1.631727849
30 0.245716270
31 -1.753689602
32 0.176776695
33 0.844713207
34 1.296112650
35 0.447361632
36 -0.198117572
37 0.620238914
38 0.297219829
39 -0.145499203
40 -0.158113883
41 0.828197543
42 0.549620159
43 -1.343528168
44 -0.543557351
45 0.177201743
46 0.497999662
47 -1.304733915
48 -0.194255768
49 0.000662151095
50 0.141421356
51 -1.424267820
52 0.0936260509
53 0.822647473
54 0.767145041
55 0.486172475
56 -0.353670424
57 -0.326607905
58 1.153805827
59 -0.725520756
60 0.173747641
61 0.601043028
62 -1.240045809
63 0.396366306
64 0.125000000
65 -0.0837416857
66 0.597302437
67 1.379909777
68 0.916490044
69 -0.547240160
70 0.316332443
71 0.0461036812
72 -0.140090278
73 0.772681596
74 0.438575142
75 -0.155404614
76 0.210166156
77 1.087474561
78 -0.102883473
79 0.109798435
80 -0.111803398
81 -0.446762566
82 0.585624099
83 -1.699950798
84 0.388640141
85 -0.819733615
86 -0.950017878
87 -1.267890187
88 -0.384353089
89 -0.580991570
90 0.125300554
91 -0.187314086
92 0.352138938
93 1.362657283
94 -0.922586199
95 -0.187978325
96 -0.137359571
97 1.508826854
98 0.000468211529
99 0.430753051
100 0.100000000
101 -1.792079919
102 -1.007109434
103 -0.0769397866
104 0.0662036155
105 -0.347610310
106 0.581699606
107 0.0538106260
108 0.542453461
109 -0.409995560
110 0.343775854
111 -0.481939947
112 -0.250082755
113 -0.949056460
114 -0.230946665
115 -0.314962641
116 0.815863924
117 -0.0741958635
118 -0.513020646
119 -1.833586842
120 0.122858135
121 0.181818379
122 0.425001601
123 -0.643528600
124 -0.876844801
125 -0.0894427190
126 0.280273302
127 0.0530061410
128 0.0883883476
129 1.043952386
130 -0.0592143138
131 -0.118751446
132 0.422356603
133 -0.420471452
134 0.975743561
135 -0.485185125
136 0.648056325
137 1.556446898
138 -0.386957228
139 0.523339136
140 0.223680816
141 1.013808356
142 0.0326002256
143 -0.203564512
144 -0.0990587860
145 -0.729730878
146 0.546368396
147 -0.000514505655
148 0.310119457
149 0.180826607
150 -0.109887656
151 -0.524030352
152 0.148609914
153 -0.726291127
154 0.768960636
155 0.784273832
156 -0.0727496018
157 0.744083070
158 0.0776392179
159 -0.639216060
160 -0.0790569415
161 -0.704511002
162 -0.315908840
163 -0.226766291
164 0.414098771
165 -0.377767230
166 -1.202046737
167 0.845648936
168 0.274810079
169 -0.964936553
170 -0.579639198
171 -0.166550415
172 -0.671764084
173 -0.913457787
174 -0.896533749
175 -0.200066204
176 -0.271778675
177 0.563746338
178 -0.410823079
179 -1.184571265
180 0.0886008717
181 -0.666741037
182 -0.132451060
183 -0.467023746
184 0.248999831
185 -0.277379275
186 0.963544205
187 -1.992657403
188 -0.652366957
189 -1.085266917
190 -0.132920748
191 -0.446739765
192 -0.0971278841
193 0.329395896
194 1.066901700
195 0.0650692219
196 0.000331075547
197 -0.557547573
198 0.304588403
199 0.893925292
200 0.0707106781
201 -1.072169071
202 -1.267191863
203 -1.632173828
204 -0.712133910
205 -0.370381201
206 -0.0544046449
207 -0.278746838
208 0.0468130254
209 -0.457292746
210 -0.245797607
211 -1.952663806
212 0.411323736
213 -0.0372700966
214 0.0380498585
215 0.600844063
216 0.383572520
217 1.754144945
218 -0.289910641
219 -0.599756106
220 0.243086237
221 0.339968931
222 -0.340783005
223 0.959965471
224 -0.176835212
225 -0.0792470288
226 -0.671084258
227 -0.961033483
228 -0.163303952
229 1.495281964
230 -0.222712219
231 -0.838795246
232 0.576902913
233 -1.265505947
234 -0.0524643982
235 0.583494745
236 -0.362760378
237 -0.186464663
238 -1.296541690